Profiling tropospheric refractivity in real time, based on a relevance vector machine and single ground-based GPS receiver

A method is developed for retrieving atmospheric refractivity profiles in real time from the slant path tropospheric delay (STD) at low elevations (<5°) of a single ground-based Global Positioning System (GPS) receiver. The technique for retrieving atmospheric profiles proposed herein is based on a relevance vector machine (RVM), which is a sparse approximate Bayesian kernel method. The RVM network is trained by using historical radiosonde data, while the simulated STDs are calculated using the ray-tracing technique. The inputs of the network are surface meteorologic parameters and differences of the STDs at various elevations, while the outputs are tropospheric refractivity profiles for specific layers. The feasibility of this method is verified by both simulation and experiment. The STDs of the GPS receiver are obtained in the experiment by the undifferenced precise point position (PPP) method with International GPS Service (IGS) ultra-rapid products, which means that this method may be applied in real time. This article proposes a new method for retrieving atmospheric refractive profiles in real time at low cost and with high efficiency.

[1]  L. Barclay.  Propagation of radiowaves , 2003 .

[2]  H. S. Hopfield.  Two- quartic tropospheric refractivity profile for correcting satellite data , 1969 .

[3]  Pierre Héroux,et al.  Precise Point Positioning Using IGS Orbit and Clock Products , 2001, GPS Solutions.

[4]  J. Wang,et al.  Impacts of Stochastic Modeling on GPS-derived ZTD Estimations , 2004 .

[5]  Victoria Anne Hoyle.  Data assimilation for 4-D wet refractivity modelling in a regional GPS network , 2005 .

[6]  Tropospheric refractivity profiling based on single ground-based GPS , 2008, 2008 International Conference on Microwave and Millimeter Wave Technology.

[7]  A. Niell.  Global mapping functions for the atmosphere delay at radio wavelengths , 1996 .

[8]  G. Ruffini,et al.  4D tropospheric tomography using GPS slant wet delays , 2000 .

[9]  Philip E. Gill,et al.  Practical optimization , 1981 .

[10]  Safaai Deris,et al.  A bayesian kernel for the prediction of protein-protein interactions , 2009 .

[11]  F. Xie.  Development of a GPS Occultation Retrieval Method for Characterizing the Marine Boundary Layer in the Presence of Super-Refraction , 2006 .

[12]  Larry J. Romans,et al.  Observing tropospheric water vapor by radio occultation using the Global Positioning System , 1995 .

[13]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[14]  Curtis F. Gerald.  Applied numerical analysis , 1970 .

[15]  Carl E. Rasmussen,et al.  Healing the relevance vector machine through augmentation , 2005, ICML.

[16]  Mauro Boccolari,et al.  GPS coordinate estimates by a priori tropospheric delays from NWP using ultra-rapid orbits , 2006 .

[17]  Daniel P. W. Ellis,et al.  Estimating single-channel source separation masks: relevance vector machine classifiers vs. pitch-based masking , 2006, SAPA@INTERSPEECH.

[18]  Vladimir Naumovich Vapni.  The Nature of Statistical Learning Theory , 1995 .

[19]  Michael E. Tipping.  Sparse Bayesian Learning and the Relevance Vector Machine , 2001, J. Mach. Learn. Res..

[20]  Anthony R. Lowry,et al.  Vertical profiling of atmospheric refractivity from ground‐based GPS , 2002 .

[21]  Curtis F. Gerald,et al.  APPLIED NUMERICAL ANALYSIS , 1972, The Mathematical Gazette.

[22]  R. Brereton,et al.  Support vector machines for classification and regression. , 2010, The Analyst.

[23]  Chen Yongqi,et al.  Wet Refractivity Tomography with an Improved Kalman-Filter Method , 2006 .

[24]  Joaquin Quiñonero Candela,et al.  Time series prediction based on the Relevance Vector Machine with adaptive kernels , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[25]  H. D. Black,et al.  Correcting satellite Doppler data for tropospheric effects , 1984 .

[26]  F. Takac,et al.  Leica System 1200 - High Performance GNSS Technology for RTK Applications , 2006 .

[27]  Leke Lin,et al.  Real time STD calculation at low elevation by GPS , 2010, Proceedings of the 9th International Symposium on Antennas, Propagation and EM Theory.